Many fields involve finding the shortest path through a lattice. For example, this problem is core to a computer system recognizing a word that has been handwritten using a stylus, determining resource allocation for a project, circuit design, or laying out pieces for a LEGO® brand building block sculpture. However, calculating an exact solution may not be feasible in computer memory or within a specified amount of time. Rather, the traditional approach is a beam search, which eliminates paths through the lattice that are unlikely to be helpful. Unfortunately, this traditional approach reduces accuracy (i.e., quality/optimality of the solution) to conserve time and memory.
There is also a need in the art for a solution to the problem of finding a less costly method for filling a fixed region with building blocks of a particular color. For example, companies, such as LEGO® hire professionals to build many of their sculptures by hand. The process can be slow, tedious, and costly. While alternative solutions using artificial intelligence (AI) have been proposed, none to date have fulfilled the long-standing need in the art.
Therefore, there is a need in the art for a system and method to generate instructions for assembling a higher-quality, less-costly LEGO® structure. More generally, there is a need in the art for a method and system for, inter alia, calculating a path through a lattice that recovers accuracy without increasing memory, and only moderately increasing time.